ManimCommunity / ManimCommunity/manim

Artifacts/false discontinuities in `ImplicitFunction`

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issue:bug
Dominant language
Python
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Description

## Description of bug / unexpected behavior
Looking closely at the output from `ImplicitFunction` you'd often see many false discontinuities. For example, if you look closely at [the example from the docs](https://docs.manim.community/en/stable/reference/manim.mobject.functions.ImplicitFunction.html#implicitfunctionexample), you'd see many points where the curve breaks.

In this example:

```py
class ImplicitFunctionDemo(Scene):
def construct(self):
plane = NumberPlane()
curve = ImplicitFunction(
lambda x, y: (x**2 + y**2)**2 - 42*(x**2 - y**2),
color=YELLOW,
max_quads=10000,
)
self.add(plane)
self.add(curve)
```

even with 10000 quads, discontinuities can still be seen:

![implicitbug](https://user-images.githubusercontent.com/9102529/136679084-11a9a9f5-1894-405f-bd62-20b606cfd929.png)

## Expected behavior

## How to reproduce the issue

Code for reproducing the problem

```py
Paste your code here.
```

## Additional media files

Images/GIFs

## Logs
Terminal output

```
PASTE HERE OR PROVIDE LINK TO https://pastebin.com/ OR SIMILAR
```

## System specifications

System Details

- OS (with version, e.g Windows 10 v2004 or macOS 10.15 (Catalina)):
- RAM:
- Python version (`python/py/python3 --version`):
- Installed modules (provide output from `pip list`):
```
PASTE HERE
```

LaTeX details

+ LaTeX distribution (e.g. TeX Live 2020):
+ Installed LaTeX packages:

FFMPEG

Output of `ffmpeg -version`:

```
PASTE HERE
```

## Additional comments

Contributor guide

Open the contributing guide

First steps

  1. Read the whole issue, then the project's contributing guide.
  2. Comment on the issue to say you are picking it up — it saves two people doing the same work.
  3. Fork the repository and make your change on a branch.
  4. Open a pull request that references the issue number.

Research direction

Start by locating the `ImplicitFunction` implementation and reproduce the documentation example with `max_quads=10000`. Trace how the curve is sampled and rendered, then verify that the false discontinuities are gone in the same example; the issue names no specific test, file, or system details.

Written by the indexing model from the issue text.

Assessment

Tech stack
python
Domain
computer-graphics
Issue type
Bug
Difficulty
4/5
Estimated time
3-5 days
Activity status
Stale
Clarity
Mostly clear
Newbie friendliness
38/100

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